In this paper, we introduce a novel two-step framework for joint angle-of-arrival (AoA) and angle-of-departure (AoD) estimation for lens antenna array (LAA)-based multipleinput and multiple-output (MIMO) systems. This method is based on the properties of the sinc function in the array response of LAAs to reduce the dimensionality of the channel matrix collected through each signal snapshot. After completing the estimation of the AoA or AoD in the first step, the remaining angle can be determined in the next step. For example, for each estimated AoA, the corresponding off-grid AoD is found. Consequently, we eliminate the need for a pairing step as seen in other methods, thereby avoiding pairing errors. Furthermore, since the proposed scheme leverages multiple snapshots, the estimation accuracy at each step can be enhanced. Simulation results indicate that the proposed method achieves the highest performance gain among all studied schemes when the number of antennas and snapshots is sufficiently large.

This paper explores two novel compressed sensing (CS) strategies for estimating the directions of incoming signals in a coherent environment using a lens antenna array (LAA). Compared to the subspace-based algorithm family, CS techniques, such as the conventional orthogonal matching pursuit (OMP), can effectively address the direction-of-arrival (DoA) estimation without prior knowledge about the number of signals at low complexity. However, they are sensitive to noise and can be adversely affected by multipath distortion. To overcome these limitations, we leverage the energy-concentrating property of an LAA and introduce the signal covariance matrix-based OMP (SCM-OMP) method. This method enhances the accuracy of angular estimation, even in regions with low signal-to-noise ratio (SNR). Furthermore, by analyzing the definition of mutual coherence (MC), we demonstrate that the SCM-OMP scheme achieves improved performance with a large number of antennas. We then propose the multiple sub-covariance matrices-based OMP (MSCM-OMP) to reduce computational complexity. We also analyze the exact recovery conditions of the studied OMP algorithms and utilize the noise reduction property to show that our proposed SCM-OMP and MSCM-OMP algorithms have better successful recovery probabilities than the OMP scheme. Moreover, we combine the Rife method with two proposed CS-based algorithms to overcome the off-grid effect. Simulation results confirm that the SCM- and MSCM-OMP schemes outperform other high-resolution DoA estimation methods in both on-grid and off-grid scenarios. Furthermore, the MSCM-OMP method can achieve a detection accuracy of higher than 60%, even in a low-SNR regime, i.e.,$\rm {SNR}=-10$dB.

This paper delves into a novel compressed sensing (CS) strategy for estimating the directions of incoming signals in a coherent environment using a lens antenna array (LAA). In comparison to the well-known subspace-based algorithm family, CS techniques, such as the conventional orthogonal matching pursuit (COMP), can effectively address the direction-of-arrival (DoA) estimation problem requiring prior knowledge about the number of signals and offer lower complexity. However, they are susceptible to noise and can be adversely affected by multipath distortion. Leveraging the energy-concentrating property of an LAA, we first introduce the signal covariance matrix-based OMP (SCM-OMP) method that enhances the angular estimation performance, even in low-SNR regions. Subsequently, we propose the multiple sub-covariance matrices-based OMP (MSCM-OMP) to achieve a reduction in computational complexity. Simulation results demonstrate that the MSCM-OMP scheme also outper-forms other high-resolution DoA estimation methods.

In this letter, we investigate a novel optimization approach to direction-of-arrival (DoA) estimation for a lens antenna array. Inspired by a property of the sinc function and${\ell _{2}}$-norm optimization, we develop the gradient descent-based spatial spectrum reconstruction (GD-SSR) to estimate the DoAs based on the sum signal covariance vector (SSCV). Our proposed algorithm does not require a priori knowledge of signal number and has a lower complexity compared with existing techniques while achieving a better estimation performance, even in a low-SNR regime. In addition, the proposed model does not require any pretraining process as prior learning-based methods. The simulation results show that our scheme not only outperforms other techniques but also resolves the angular ambiguity problem.

This work explores the potential of a deep learning-aided detector for narrowband signal enumeration in a coherent environment. Specifically, we introduce the logarithmic eigenvalue-based classification network (LogECNet) to detect the signal number. In the proposed scheme, the full-row Toeplitz matrices reconstruction (FTMR) algorithm is employed to avoid the rank loss of the signal covariance matrix (SCM) in highly correlated signal environments. The simulation results show that the FTMR method not only achieves the complexity reduction with respect to the prior forward/backward spatial smoothing (FBSS) algorithm, but also improves the signal number detection performance when combined with LogECNet.